Can the current successes of global machine learning-based weather simulators be generalized beyond two-week forecasts to stable and accurate multiyear runs? The recently developed AI2 Climate Emulator (ACE) suggests this is feasible, based upon 10-year simulations trained on a realistic global atmosphere model using a grid spacing of approximately 110~km and forced by a repeating annual cycle of sea-surface temperature. Here we show that ACE, without modification, can be trained to emulate another major atmospheric model, EAMv2, run at a comparable grid spacing for at least ten years with similarly small climate biases. ACE accurately reproduces EAMv2’s frequency distribution of daily-mean precipitation, its time-mean spatial pattern of precipitation, and its space-time structure of tropical precipitation, including the Madden-Julian Oscillation. Moreover, ACE’s climate biases with respect to EAMv2 are substantially smaller than EAMv2’s own biases compared to the observed historical average surface precipitation rate and top-of-atmosphere radiative fluxes.